Kosmoceratops, a relative of the more familiar Triceratops, had one horn over its nose, one over each eye, one protruding from each cheek bone and a row of ten across the frill at the back of its head.

"As far as we know it's the most ornate-headed dinosaur ever found, with so many well-developed horns on its head," Sampson told the Guardian.

Scientists have long speculated about the purpose of dinosaurs' horns. In the past, some suspected that beasts like Triceratops used their headgear to fight off predators, as depicted in the prehistoric clash between a fur-bikinied Raquel Welch and a Triceratops in Ray Harryhausen's 1966 movie, One Million Years BC. Many palaeontologists now believe that dinosaurs' horns were often more for sexual display and fighting off other members of the same species, much like rutting deer.

"In this case, we think these horns were really about competing for mates and more akin to peacock feathers or deer antlers, where it's males trying to attract females or intimidate other males," Sampson said. "Sometimes it's good to have a way of visually ranking yourself relative to other animals. You can avoid unnecessary conflicts and that is probably what they were doing with all these bony bells and whistles."

"This is one of the last, largely unexplored dinosaur treasure troves on the continent. We have to hike many miles to find these specimens in the first place and have to use helicopters to get them out," Sampson said.

North America looked very different when the plant-eating Kosmoceratops roamed the land. A warm, shallow sea flooded much of central North America, dividing the continent into two land masses: Laramidia in the west and Appalachia in the east.

Kosmoceratops lived in Laramidia, an area known as the "lost continent", alongside other herbivores, including armoured ankylosaurs, duck-billed hadrosaurs and dome-headed pachycephalosaurs, and carnivorous predators such as raptors and tyrannosaurs.

"At the time, this was very much a swamp environment and very lush. The climate was more Mediterranean. It would have been a great place to hang out except for all the tyrannosaurs," said Sampson.

The remains of other fossilised skulls uncovered at the site belong to another new relative of Triceratops. The animal, named Utahceratops, was even larger than Kosmoceratops, but had a more familiar arrangement of horns, with one large one over its nose and two blunt outward-pointing horns above its eyes. Both species are described in the journal PLoS ONE.

According to Sampson, both males and females of either species have similar horns. "The most obvious explanation is that the females don't want predators to pick them off so they mimic the males," he said.

• This article was amended on 3 July 2012. The original referred to the Giant Staircase-Escalante National Monument. This has been corrected.